I find the information on the remaining time for my next move(s) a bit cryptic.
E.g. when it says “2 Days 14 Hours/5” what does this mean?

I also notice a difference in the format of my remaining time and that for my opponent.
When it says “2 Days 14 Hours/5” for me, it says “2 Days 19 Hours + 4d/10” for my opponent. Why a “+” sign and a (supposedly) number of days indication before the “/10”?

Maybe it is an idea to explain this in a help section, because I couldn’t find it anywhere.

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You do need to know how the game timing that you have chosen works. That page ^^ simply points to Senseis for more about that.

I think that if you read up on how the timing system works, the notation becomes reasonably obvious.

For example, if you know that Canadian timing has a set period of time to play a certain number of stones, which resets each time you play that many stones, then it might be clear that “2 Days 14 Hours/5” means “You have 2 days 14 hours to play your 5 stones before you get your time reset”.

I understand that. But I don’t understand why I don’t see that my opponent also needs to play his x stones in a certain time period. Why does it say that he has 2 Days 19 Hours? Is this because the number of stones is equal for him? Is the “+ 4d/10” applicable to both players, but mentionned only for the player with the least of time remaining / player that started the time period?

In your case the time control is
“Main time” + 4d/10
The main time is like absolute time. Each player plays as many moves as he likes until the main time reaches 0.
After the clock of the player reached 0 the 4d/10 starts.

I wish during live games we could just show ‘remaining time’ ‘remaining moves’, as minor as it is, that’s all anyone needs to know. Showing ‘moves made’/‘moves per period’ just seems weird when we are counting up in moves and down in time.

Also, time control is shown in one format on one screen, and other on the next
I.e. on profile page it is shown “5 days 6 hours/2”, but on the game page it is shown as “5 days 6 hours/ 8/10”

Lastly, it is also confusing if you are finishing main time or finishing a period… If you are on the last day of main time it would show “1 day + 5 days/0/10”. If you are out of main time, and have not played any of your 10 moves and are 1 day from timing out it will show “1 day + 5 days/0/10” iirc?

It makes sense now. If I add the 4 days (main time) and the time that I used in the first extra period and the time that my opponent used of his main time, it all adds up to the total time of the game.